Question

(x+2)^2+(y-1)^2=9 y=x-1 решите систему

Answer 1

Ответ: х = 1, у = 0

Пошаговое объяснение:

Применим метод подстановки:   y-1 = x-2

(x²+4x+4) + (x²-4x+4) = 9

2x² = 1,  

х = 1,  у = х-1 = 0 - ответ

Answer 2

To solve the system of equations:

1. (x+2)^2 + (y-1)^2 = 9
2. y = x - 1

We can use substitution. Since the second equation already expresses y in terms of x, we can substitute this value of y into the first equation.

Step 1: Substitute y from equation (2) into equation (1):

(x + 2)^2 + (x - 1 - 1)^2 = 9

Step 2: Simplify the equation:

(x + 2)^2 + (x - 2)^2 = 9

Step 3: Expand and combine like terms:

x^2 + 4x + 4 + x^2 - 4x + 4 = 9

Step 4: Simplify further:

2x^2 + 8 = 9

Step 5: Move constant term to the other side:

2x^2 = 9 - 8

Step 6: Solve for x:

2x^2 = 1

x^2 = 1/2

Step 7: Take the square root of both sides:

x = ±√(1/2)

So, x can have two possible values:

x = √(1/2) or x = -√(1/2)

Step 8: Substitute the values of x back into the second equation (y = x - 1) to find the corresponding values of y:

For x = √(1/2):

y = √(1/2) - 1 ≈ -0.293

For x = -√(1/2):

y = -√(1/2) - 1 ≈ -1.707

Thus, the solutions to the system of equations are approximately:

1. (x ≈ √(1/2), y ≈ -0.293)
2. (x ≈ -√(1/2), y ≈ -1.707)